exploratory
Jiner Zheng
2022-04-19
Variables from Prosperity Index
persfreedomagency: Pillar of Personal Freedom –> the degree to which citizens are free from restriction and are free to move, indicating the experiences of the freedom to act independently and making free choices
- its indicators consist of e.g. personal autonomy and individual rights, freedom of movement, satisfaction with freedom, etc.)
Socialcapsocialnetwork: Social network (pillar of Social capital)
- the strength and opportunities of the individuals’ relationships with wider social network, including social support (e.g. respect, opportunity to make friends or helping another household)
Healthprevent: Preventative interventions (pillar of Health)
- the extent to which the health system prevents diseases and other medical complications from occurring (e.g. the existence of national screening programs, or diphteria, measles, hepatitis immunization, etc.)
Socialcapcivic: Civic and social participation (pillar of Social capital)
- the amount to which citizens participate within the society, split into the civic and social spheres (e.g. donated money to charity, volunteering, etc.)
PersonalFreedom: Freedom of assembly and association (pillar of Personal Freedom)
- the degree to which citizens have the freedom to assemble with others in public spaces, or to express their opinions
GovernanGovernmeffect: Government effectiveness (pillar of Governance)
- the quality of public health provision, the competence of officials and the quality of the bureaucracy (e.g. policy coordination, government quality and credibility, efficiency of government spending, etc.)
Socialcappersonalandfamily: Personal and family relationships (pillar of Social capital)
- the strength of the closest personal relationships and family ties, forming the individual’s emotional, mental and financial support (e.g. help from family and friends when in trouble or the positive energy provided by the family)
Clustering using gower distance
| location | stringency_class | excess_death_class | persfreedomagency | Socialcapsocialnetwork | healthprevent | Socialcapcivic | PersonalFreedom | GovernanGovernmeffect | Socialcappersonalandfamily | continent | population | population_density | median_age | aged_65_older | gdp_per_capita | life_expectancy | Climateclass | cum_p_score | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 64 | Switzerland | 2 | 1 | 22.4 | 15.4 | 13.8 | 10.7 | 18.8 | 19.1 | 17.1 | Europe | 8715494 | 214.243 | 43.1 | 18.436 | 57410.17 | 83.78 | Class C - Temperate (Mesothermal) Climates | 0.0772404 |
| 3 | Austria | 2 | 1 | 22.1 | 14.6 | 13.2 | 12.2 | 17.7 | 17.9 | 16.2 | Europe | 9043072 | 106.749 | 44.4 | 19.202 | 45436.69 | 81.54 | Class C - Temperate (Mesothermal) Climates | 0.0845804 |
| location | stringency_class | excess_death_class | persfreedomagency | Socialcapsocialnetwork | healthprevent | Socialcapcivic | PersonalFreedom | GovernanGovernmeffect | Socialcappersonalandfamily | continent | population | population_density | median_age | aged_65_older | gdp_per_capita | life_expectancy | Climateclass | cum_p_score | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 18 | Egypt | 1 | 4 | 8.7 | 14.9 | 12.5 | 0.8 | 2.1 | 7.3 | 9.9 | Africa | 104258327 | 97.999 | 25.3 | 5.159 | 10550.21 | 71.99 | Class B - Dry (Arid and Semiarid) Climates | 0.1983465 |
| 16 | Denmark | 2 | 3 | 22.9 | 16.0 | 13.8 | 11.7 | 19.5 | 18.6 | 18.3 | Europe | 5813302 | 136.520 | 42.3 | 19.677 | 46682.51 | 80.90 | Class C - Temperate (Mesothermal) Climates | 0.0071318 |
Pick number of clusters using the silhouette figure
2 clusters has the highest silhouette width. 3 is simpler and almost as good. Let’s pick k = 3
Interpretation
Summary of each cluster
## [[1]]
## location stringency_class excess_death_class persfreedomagency
## Length:20 1:10 1:17 Min. : 9.40
## Class :character 2: 4 2: 1 1st Qu.:14.70
## Mode :character 3: 5 3: 2 Median :16.40
## 4: 1 4: 0 Mean :16.23
## 3rd Qu.:18.07
## Max. :20.90
## Socialcapsocialnetwork healthprevent Socialcapcivic PersonalFreedom
## Min. : 8.50 Min. : 9.20 Min. : 4.100 Min. : 5.40
## 1st Qu.:12.20 1st Qu.:11.75 1st Qu.: 4.575 1st Qu.:12.38
## Median :13.00 Median :12.65 Median : 5.650 Median :13.45
## Mean :12.92 Mean :12.33 Mean : 5.945 Mean :13.84
## 3rd Qu.:13.82 3rd Qu.:13.20 3rd Qu.: 6.825 3rd Qu.:16.07
## Max. :15.80 Max. :14.00 Max. :10.100 Max. :18.30
## GovernanGovernmeffect Socialcappersonalandfamily continent
## Min. : 5.900 Min. :10.60 Africa : 1
## 1st Qu.: 9.525 1st Qu.:14.65 Asia : 4
## Median :11.450 Median :15.60 Europe :14
## Mean :11.210 Mean :15.06 North America: 0
## 3rd Qu.:13.200 3rd Qu.:16.12 Oceania : 0
## Max. :16.000 Max. :17.30 South America: 1
## population population_density median_age aged_65_older
## Min. : 98910 Min. : 8.823 Min. :26.30 Min. : 4.489
## 1st Qu.: 3165828 1st Qu.: 56.857 1st Qu.:37.52 1st Qu.:13.359
## Median : 5355002 Median : 78.841 Median :41.30 Median :15.663
## Mean : 18015135 Mean :127.877 Mean :39.62 Mean :15.000
## 3rd Qu.: 12007564 3rd Qu.:123.748 3rd Qu.:43.10 3rd Qu.:18.032
## Max. :145912022 Max. :594.561 Max. :44.70 Max. :20.801
## gdp_per_capita life_expectancy
## Min. : 3393 Min. :71.45
## 1st Qu.:11781 1st Qu.:73.68
## Median :21611 Median :76.47
## Mean :19515 Mean :76.36
## 3rd Qu.:26481 3rd Qu.:78.61
## Max. :35938 Max. :83.03
## Climateclass cum_p_score
## : 0 Min. :-0.06918
## Class A - Tropical Climates : 1 1st Qu.: 0.10505
## Class B - Dry (Arid and Semiarid) Climates : 0 Median : 0.16355
## Class C - Temperate (Mesothermal) Climates :16 Mean : 0.14279
## Class D - Continental (Microthermal) Climates: 3 3rd Qu.: 0.20348
## Max. : 0.25187
## cluster
## Min. :1
## 1st Qu.:1
## Median :1
## Mean :1
## 3rd Qu.:1
## Max. :1
##
## [[2]]
## location stringency_class excess_death_class persfreedomagency
## Length:28 1: 5 1:10 Min. :15.00
## Class :character 2:14 2: 1 1st Qu.:20.02
## Mode :character 3: 6 3:10 Median :21.10
## 4: 3 4: 7 Mean :20.86
## 3rd Qu.:21.95
## Max. :23.80
## Socialcapsocialnetwork healthprevent Socialcapcivic PersonalFreedom
## Min. : 5.10 Min. :12.60 Min. : 4.100 Min. :12.00
## 1st Qu.:13.45 1st Qu.:13.20 1st Qu.: 6.675 1st Qu.:17.30
## Median :14.65 Median :13.60 Median : 9.450 Median :17.95
## Mean :13.98 Mean :13.51 Mean : 9.357 Mean :17.65
## 3rd Qu.:15.70 3rd Qu.:13.82 3rd Qu.:12.200 3rd Qu.:18.43
## Max. :16.40 Max. :14.10 Max. :14.000 Max. :19.50
## GovernanGovernmeffect Socialcappersonalandfamily continent
## Min. :12.10 Min. :12.10 Africa : 0
## 1st Qu.:17.68 1st Qu.:15.78 Asia : 3
## Median :18.20 Median :16.20 Europe :22
## Mean :17.44 Mean :16.18 North America: 1
## 3rd Qu.:18.73 3rd Qu.:17.10 Oceania : 2
## Max. :19.10 Max. :18.30 South America: 0
## population population_density median_age aged_65_older
## Min. : 368792 Min. : 3.202 Min. :30.60 Min. :11.73
## 1st Qu.: 5368528 1st Qu.: 42.753 1st Qu.:39.70 1st Qu.:15.48
## Median : 9167036 Median : 112.750 Median :42.60 Median :18.89
## Mean : 31695700 Mean : 443.128 Mean :42.10 Mean :18.31
## 3rd Qu.: 19326875 3rd Qu.: 245.987 3rd Qu.:44.58 3rd Qu.:19.75
## Max. :332915074 Max. :7039.714 Max. :48.20 Max. :27.05
## gdp_per_capita life_expectancy
## Min. :24574 Min. :75.93
## 1st Qu.:33987 1st Qu.:81.33
## Median :41622 Median :82.27
## Mean :43980 Mean :81.88
## 3rd Qu.:47330 3rd Qu.:82.97
## Max. :94278 Max. :84.86
## Climateclass cum_p_score
## : 0 Min. :-0.04109
## Class A - Tropical Climates : 1 1st Qu.: 0.02111
## Class B - Dry (Arid and Semiarid) Climates : 1 Median : 0.07470
## Class C - Temperate (Mesothermal) Climates :22 Mean : 0.06771
## Class D - Continental (Microthermal) Climates: 4 3rd Qu.: 0.10185
## Max. : 0.18554
## cluster
## Min. :2
## 1st Qu.:2
## Median :2
## Mean :2
## 3rd Qu.:2
## Max. :2
##
## [[3]]
## location stringency_class excess_death_class persfreedomagency
## Length:22 1:12 1: 0 Min. : 5.70
## Class :character 2: 2 2:14 1st Qu.:12.25
## Mode :character 3: 7 3: 4 Median :15.25
## 4: 1 4: 4 Mean :14.02
## 3rd Qu.:15.88
## Max. :20.00
## Socialcapsocialnetwork healthprevent Socialcapcivic PersonalFreedom
## Min. :10.10 Min. : 9.80 Min. : 0.800 Min. : 1.700
## 1st Qu.:14.00 1st Qu.:12.05 1st Qu.: 4.275 1st Qu.: 3.775
## Median :15.00 Median :13.45 Median : 6.150 Median :12.400
## Mean :14.55 Mean :12.84 Mean : 6.027 Mean :10.041
## 3rd Qu.:15.50 3rd Qu.:13.70 3rd Qu.: 8.200 3rd Qu.:14.675
## Max. :16.30 Max. :14.40 Max. :10.700 Max. :17.500
## GovernanGovernmeffect Socialcappersonalandfamily continent
## Min. : 5.200 Min. : 9.70 Africa :3
## 1st Qu.: 8.475 1st Qu.:14.50 Asia :9
## Median : 9.900 Median :15.80 Europe :0
## Mean :10.105 Mean :15.16 North America:3
## 3rd Qu.:11.825 3rd Qu.:16.50 Oceania :0
## Max. :15.000 Max. :18.00 South America:7
## population population_density median_age aged_65_older
## Min. : 1273428 Min. : 1.98 Min. :22.90 Min. : 1.307
## 1st Qu.: 5895110 1st Qu.: 24.47 1st Qu.:28.12 1st Qu.: 5.205
## Median : 18622413 Median : 58.14 Median :30.65 Median : 6.780
## Mean : 41321248 Mean : 447.64 Mean :31.06 Mean : 6.909
## 3rd Qu.: 57847957 3rd Qu.: 113.98 3rd Qu.:33.23 3rd Qu.: 8.325
## Max. :213993441 Max. :7915.73 Max. :42.40 Max. :12.922
## gdp_per_capita life_expectancy
## Min. : 6253 Min. :64.13
## 1st Qu.: 10897 1st Qu.:73.15
## Median : 14814 Median :75.47
## Mean : 22994 Mean :75.33
## 3rd Qu.: 19990 3rd Qu.:77.25
## Max. :116936 Max. :83.62
## Climateclass cum_p_score
## : 0 Min. :0.02013
## Class A - Tropical Climates :10 1st Qu.:0.11462
## Class B - Dry (Arid and Semiarid) Climates : 9 Median :0.19834
## Class C - Temperate (Mesothermal) Climates : 1 Mean :0.19346
## Class D - Continental (Microthermal) Climates: 2 3rd Qu.:0.24568
## Max. :0.45778
## cluster
## Min. :3
## 1st Qu.:3
## Median :3
## Mean :3
## 3rd Qu.:3
## Max. :3## location stringency_class excess_death_class persfreedomagency
## Length:70 1:27 1:27 Min. : 5.70
## Class :character 2:20 2:16 1st Qu.:15.22
## Mode :character 3:18 3:16 Median :17.60
## 4: 5 4:11 Mean :17.39
## 3rd Qu.:20.88
## Max. :23.80
## Socialcapsocialnetwork healthprevent Socialcapcivic PersonalFreedom
## Min. : 5.10 Min. : 9.20 Min. : 0.800 Min. : 1.70
## 1st Qu.:12.88 1st Qu.:12.53 1st Qu.: 4.925 1st Qu.:12.40
## Median :14.40 Median :13.30 Median : 6.850 Median :16.00
## Mean :13.86 Mean :12.96 Mean : 7.336 Mean :14.17
## 3rd Qu.:15.40 3rd Qu.:13.78 3rd Qu.: 9.100 3rd Qu.:17.70
## Max. :16.40 Max. :14.40 Max. :14.000 Max. :19.50
## GovernanGovernmeffect Socialcappersonalandfamily continent
## Min. : 5.20 Min. : 9.70 Africa : 4
## 1st Qu.: 9.95 1st Qu.:14.93 Asia :16
## Median :12.85 Median :16.00 Europe :36
## Mean :13.35 Mean :15.54 North America: 4
## 3rd Qu.:17.90 3rd Qu.:16.50 Oceania : 2
## Max. :19.10 Max. :18.30 South America: 8
## population population_density median_age aged_65_older
## Min. : 98910 Min. : 1.98 Min. :22.90 Min. : 1.307
## 1st Qu.: 4306969 1st Qu.: 31.49 1st Qu.:32.40 1st Qu.: 8.524
## Median : 9167036 Median : 84.30 Median :39.65 Median :14.759
## Mean : 30812139 Mean : 354.48 Mean :37.92 Mean :13.780
## 3rd Qu.: 33791678 3rd Qu.: 152.67 3rd Qu.:43.08 3rd Qu.:18.946
## Max. :332915074 Max. :7915.73 Max. :48.20 Max. :27.049
## gdp_per_capita life_expectancy
## Min. : 3393 Min. :64.13
## 1st Qu.: 14063 1st Qu.:75.11
## Median : 26580 Median :78.65
## Mean : 30394 Mean :78.24
## 3rd Qu.: 39565 3rd Qu.:82.19
## Max. :116936 Max. :84.86
## Climateclass cum_p_score
## : 0 Min. :-0.06918
## Class A - Tropical Climates :12 1st Qu.: 0.05075
## Class B - Dry (Arid and Semiarid) Climates :10 Median : 0.11256
## Class C - Temperate (Mesothermal) Climates :39 Mean : 0.12868
## Class D - Continental (Microthermal) Climates: 9 3rd Qu.: 0.19609
## Max. : 0.45778
## cluster
## Min. :1.000
## 1st Qu.:1.000
## Median :2.000
## Mean :2.029
## 3rd Qu.:3.000
## Max. :3.000
Cluster 1: 19 Countries
| location | excess_death_class | stringency_class | Climateclass |
|---|---|---|---|
| Albania | 1 | 1 | Class C - Temperate (Mesothermal) Climates |
| Bosnia and Herzegovina | 1 | 1 | Class C - Temperate (Mesothermal) Climates |
| Bulgaria | 1 | 2 | Class C - Temperate (Mesothermal) Climates |
| Croatia | 1 | 1 | Class C - Temperate (Mesothermal) Climates |
| Estonia | 1 | 1 | Class D - Continental (Microthermal) Climates |
| Georgia | 1 | 2 | Class C - Temperate (Mesothermal) Climates |
| Hungary | 1 | 3 | Class C - Temperate (Mesothermal) Climates |
| Kyrgyzstan | 1 | 1 | Class C - Temperate (Mesothermal) Climates |
| Latvia | 1 | 1 | Class C - Temperate (Mesothermal) Climates |
| Lebanon | 1 | 3 | Class C - Temperate (Mesothermal) Climates |
| Moldova | 1 | 3 | Class C - Temperate (Mesothermal) Climates |
| Poland | 1 | 2 | Class C - Temperate (Mesothermal) Climates |
| Russia | 1 | 1 | Class D - Continental (Microthermal) Climates |
| Serbia | 1 | 1 | Class C - Temperate (Mesothermal) Climates |
| Seychelles | 1 | 4 | Class A - Tropical Climates |
| Ukraine | 1 | 1 | Class D - Continental (Microthermal) Climates |
| Uruguay | 1 | 3 | Class C - Temperate (Mesothermal) Climates |
| Romania | 2 | 2 | Class C - Temperate (Mesothermal) Climates |
| Cyprus | 3 | 1 | Class C - Temperate (Mesothermal) Climates |
| South Korea | 3 | 3 | Class C - Temperate (Mesothermal) Climates |
|
|
|
|
Cluster 1 countries profile – other variables
58% (11/19 countries) in Excess Death Class 4 (e.g. Russia, Hungary, Ukraine)
63% (12/19 countries) in Stringency Class 1
68% (13/19 countries) in Temperate (Mesothermal) Climates
Cluster 2: 27 Countries
| location | excess_death_class | stringency_class | Climateclass |
|---|---|---|---|
| Austria | 1 | 2 | Class C - Temperate (Mesothermal) Climates |
| Czechia | 1 | 2 | Class C - Temperate (Mesothermal) Climates |
| Israel | 1 | 2 | Class C - Temperate (Mesothermal) Climates |
| Lithuania | 1 | 2 | Class D - Continental (Microthermal) Climates |
| Luxembourg | 1 | 1 | Class C - Temperate (Mesothermal) Climates |
| Malta | 1 | 1 | Class C - Temperate (Mesothermal) Climates |
| Slovakia | 1 | 2 | Class C - Temperate (Mesothermal) Climates |
| Slovenia | 1 | 2 | Class C - Temperate (Mesothermal) Climates |
| Switzerland | 1 | 2 | Class C - Temperate (Mesothermal) Climates |
| United States | 1 | 3 | Class C - Temperate (Mesothermal) Climates |
| Portugal | 2 | 3 | Class C - Temperate (Mesothermal) Climates |
| Australia | 3 | 2 | Class B - Dry (Arid and Semiarid) Climates |
| Denmark | 3 | 2 | Class C - Temperate (Mesothermal) Climates |
| Finland | 3 | 1 | Class D - Continental (Microthermal) Climates |
| Germany | 3 | 4 | Class C - Temperate (Mesothermal) Climates |
| Greece | 3 | 4 | Class C - Temperate (Mesothermal) Climates |
| Hong Kong | 3 | 2 | Class A - Tropical Climates |
| Iceland | 3 | 2 | Class C - Temperate (Mesothermal) Climates |
| Japan | 3 | 4 | Class C - Temperate (Mesothermal) Climates |
| New Zealand | 3 | 1 | Class C - Temperate (Mesothermal) Climates |
| Norway | 3 | 3 | Class D - Continental (Microthermal) Climates |
| Belgium | 4 | 1 | Class C - Temperate (Mesothermal) Climates |
| Ireland | 4 | 2 | Class C - Temperate (Mesothermal) Climates |
| Italy | 4 | 2 | Class C - Temperate (Mesothermal) Climates |
| Netherlands | 4 | 2 | Class C - Temperate (Mesothermal) Climates |
| Spain | 4 | 3 | Class C - Temperate (Mesothermal) Climates |
| Sweden | 4 | 3 | Class D - Continental (Microthermal) Climates |
| United Kingdom | 4 | 3 | Class C - Temperate (Mesothermal) Climates |
Most in Excess Death Class 1 & 2 (e.g. Russia, Hungary, Ukraine)
48% in Stringency Class 3
85% (23/27 countries) in Temperate (Mesothermal) Climates
|
|
|
|
Cluster 2 countries profile – other variables
Cluster 3: 20 Countries
| location | excess_death_class | stringency_class | Climateclass |
|---|---|---|---|
| Azerbaijan | 2 | 3 | Class B - Dry (Arid and Semiarid) Climates |
| Brazil | 2 | 3 | Class A - Tropical Climates |
| Colombia | 2 | 3 | Class A - Tropical Climates |
| Costa Rica | 2 | 1 | Class A - Tropical Climates |
| Ecuador | 2 | 1 | Class A - Tropical Climates |
| Guatemala | 2 | 1 | Class A - Tropical Climates |
| Iran | 2 | 4 | Class B - Dry (Arid and Semiarid) Climates |
| Mexico | 2 | 3 | Class B - Dry (Arid and Semiarid) Climates |
| Oman | 2 | 3 | Class B - Dry (Arid and Semiarid) Climates |
| Paraguay | 2 | 1 | Class C - Temperate (Mesothermal) Climates |
| Peru | 2 | 1 | Class A - Tropical Climates |
| Qatar | 2 | 2 | Class B - Dry (Arid and Semiarid) Climates |
| South Africa | 2 | 1 | Class B - Dry (Arid and Semiarid) Climates |
| Uzbekistan | 2 | 1 | Class B - Dry (Arid and Semiarid) Climates |
| Mauritius | 3 | 2 | Class A - Tropical Climates |
| Mongolia | 3 | 3 | Class D - Continental (Microthermal) Climates |
| Singapore | 3 | 1 | Class A - Tropical Climates |
| Thailand | 3 | 1 | Class A - Tropical Climates |
| Bolivia | 4 | 1 | Class A - Tropical Climates |
| Chile | 4 | 3 | Class B - Dry (Arid and Semiarid) Climates |
| Egypt | 4 | 1 | Class B - Dry (Arid and Semiarid) Climates |
| Kazakhstan | 4 | 1 | Class D - Continental (Microthermal) Climates |
|
|
|
|
Cluster 3 countries profile – other variables
All 3 Clusters Profiles Together
| Cluster 1 | Cluster 2 | Cluster 3 | |
|---|---|---|---|
| Number of Countries | 28 | 21 | 21 |
| Personal Freedom | 16.4 | 21.1 | 15.25 |
| Social Network | 13 | 14.65 | 15 |
| Assembly Freedom | 13.45 | 17.95 | 12.4 |
| Health Preventions | 12.65 | 13.6 | 13.45 |
| Social & Civic Participartion | 5.65 | 9.45 | 6.15 |
| Government Effect | 11.45 | 18.2 | 9.9 |
| Personal & Family Relationships | 15.6 | 16.2 | 15.8 |
| Population Density | 78.84 | 112.75 | 58.14 |
| Median Age | 41.3 | 42.6 | 30.65 |
| Aged 65 Older | 15.66 | 18.89 | 6.78 |
| GDP per capita | 21610.6 | 41622.15 | 14814.22 |
| Life Expectancy | 76.47 | 82.26 | 75.47 |
| Dominate Climate Class | Temperate (21) | Temperate (16) | Tropical (8) & Dry (8) |
| Excess Death Class | Class 1 (23) | Class 3 (12) & Class 4 (6) | Class 2 (14) |
| Stringency Class | Class 2 (14) | Class 1 (7) & Class 3 (6) | Class 1 (13) |
Multinomial Regression (DV – membership)
Model Summary
library(rsample)
data2$cluster <- relevel(as.factor(data2$cluster), ref = 2)
#data3 <- cbind(data2[c(2,3,17,18)], data2_mat[-1])
data_split <- initial_split(data2, prop = .75)
data_train <- training(data_split)[-1]
data_test <- testing(data_split)[-1]library(nnet)
# Run a "only intercept" model
OIM <- multinom(cluster ~ 1, data = data_train)## # weights: 6 (2 variable)
## initial value 57.127839
## final value 57.108728
## convergedsummary(OIM)## Call:
## multinom(formula = cluster ~ 1, data = data_train)
##
## Coefficients:
## (Intercept)
## 1 5.71584e-02
## 3 -8.54984e-09
##
## Std. Errors:
## (Intercept)
## 1 0.3381998
## 3 0.3429972
##
## Residual Deviance: 114.2175
## AIC: 118.2175model <- multinom(cluster ~ ., data = data_train)## # weights: 93 (60 variable)
## initial value 57.127839
## iter 10 value 34.726399
## iter 20 value 8.900943
## iter 30 value 5.284605
## iter 40 value 0.616017
## iter 50 value 0.131827
## iter 60 value 0.061905
## iter 70 value 0.024493
## iter 80 value 0.005463
## final value 0.000075
## convergedsummary(model)## Call:
## multinom(formula = cluster ~ ., data = data_train)
##
## Coefficients:
## (Intercept) stringency_class2 stringency_class3 stringency_class4
## 1 22.860238 -129.94600 1.058738 -209.86182
## 3 -4.224633 3.92066 -7.469922 -56.32008
## excess_death_class2 excess_death_class3 excess_death_class4 persfreedomagency
## 1 -29.37746 -131.29702 -54.680141 -2.493351
## 3 44.07459 50.33522 4.881733 136.374016
## Socialcapsocialnetwork healthprevent Socialcapcivic PersonalFreedom
## 1 75.66182 92.53841 18.468824 1.618292
## 3 169.31903 30.86458 6.449642 -131.393097
## GovernanGovernmeffect Socialcappersonalandfamily continentAsia
## 1 34.149578 -47.67178 -8.917245
## 3 1.526353 -43.78987 51.850091
## continentEurope continentNorth America continentOceania
## 1 11.74689 -34.90204 -1.842880
## 3 -36.57126 34.26249 -1.278195
## continentSouth America population population_density median_age
## 1 0.4570643 -4.818798e-07 1.1655735 3.065139
## 3 3.6549983 7.085976e-06 0.8644428 -129.304930
## aged_65_older gdp_per_capita life_expectancy
## 1 -30.76342 -0.06530090 3.142173
## 3 -137.71957 -0.02060771 55.873130
## ClimateclassClass A - Tropical Climates
## 1 -33.68206
## 3 31.26904
## ClimateclassClass B - Dry (Arid and Semiarid) Climates
## 1 -5.055084
## 3 13.188124
## ClimateclassClass C - Temperate (Mesothermal) Climates
## 1 39.77158
## 3 -29.47337
## ClimateclassClass D - Continental (Microthermal) Climates cum_p_score
## 1 21.82580 -13.277662
## 3 -19.20843 2.120371
##
## Std. Errors:
## (Intercept) stringency_class2 stringency_class3 stringency_class4
## 1 2.363847e-07 4.452977e-08 2.606673e-08 7.046433e-08
## 3 8.659380e-21 9.175819e-44 2.046525e-41 8.659380e-21
## excess_death_class2 excess_death_class3 excess_death_class4 persfreedomagency
## 1 4.452977e-08 7.046433e-08 2.606673e-08 4.532761e-06
## 3 4.133388e-114 9.175819e-44 2.046525e-41 1.376841e-19
## Socialcapsocialnetwork healthprevent Socialcapcivic PersonalFreedom
## 1 3.175240e-06 2.980414e-06 1.152044e-06 4.054232e-06
## 3 1.194994e-19 1.203654e-19 8.745973e-20 1.117060e-19
## GovernanGovernmeffect Socialcappersonalandfamily continentAsia
## 1 3.178366e-06 3.858797e-06 1.670647e-24
## 3 9.958287e-20 1.394160e-19 1.098913e-97
## continentEurope continentNorth America continentOceania
## 1 2.363847e-07 4.133388e-114 7.376054e-28
## 3 3.529905e-91 4.133388e-114 9.175819e-44
## continentSouth America population population_density median_age
## 1 2.046525e-41 6.707649e-06 7.135551e-06 1.033972e-05
## 3 2.046525e-41 8.564992e-16 1.804216e-18 3.134695e-19
## aged_65_older gdp_per_capita life_expectancy
## 1 4.617710e-06 6.080739e-03 1.867252e-05
## 3 7.452262e-20 2.284542e-16 6.355985e-19
## ClimateclassClass A - Tropical Climates
## 1 8.65938e-21
## 3 8.65938e-21
## ClimateclassClass B - Dry (Arid and Semiarid) Climates
## 1 2.046525e-41
## 3 2.055701e-41
## ClimateclassClass C - Temperate (Mesothermal) Climates
## 1 8.892737e-08
## 3 4.752105e-97
## ClimateclassClass D - Continental (Microthermal) Climates cum_p_score
## 1 1.474574e-07 2.456626e-08
## 3 3.529903e-91 5.990356e-22
##
## Residual Deviance: 0.0001499407
## AIC: 116.0001Interpretation of the Model Fit information
## Model
## 1 1
## 2 stringency_class + excess_death_class + persfreedomagency + Socialcapsocialnetwork + healthprevent + Socialcapcivic + PersonalFreedom + GovernanGovernmeffect + Socialcappersonalandfamily + continent + population + population_density + median_age + aged_65_older + gdp_per_capita + life_expectancy + Climateclass + cum_p_score
## Resid. df Resid. Dev Test Df LR stat. Pr(Chi)
## 1 102 1.142175e+02 NA NA NA
## 2 46 1.499407e-04 1 vs 2 56 114.2173 7.220232e-06Get p-values
# Calculate z-score for the model (wald Z)
zvalues <- summary(model)$coefficients / summary(model)$standard.errors
# Calculate p-values
#pnorm(abs(zvalues), lower.tail = FALSE)*2
# 2-tailed z test
p <- (1 - pnorm(abs(zvalues), 0, 1)) * 2
p## (Intercept) stringency_class2 stringency_class3 stringency_class4
## 1 0 0 0 0
## 3 0 0 0 0
## excess_death_class2 excess_death_class3 excess_death_class4 persfreedomagency
## 1 0 0 0 0
## 3 0 0 0 0
## Socialcapsocialnetwork healthprevent Socialcapcivic PersonalFreedom
## 1 0 0 0 0
## 3 0 0 0 0
## GovernanGovernmeffect Socialcappersonalandfamily continentAsia
## 1 0 0 0
## 3 0 0 0
## continentEurope continentNorth America continentOceania
## 1 0 0 0
## 3 0 0 0
## continentSouth America population population_density median_age aged_65_older
## 1 0 0.942729 0 0 0
## 3 0 0.000000 0 0 0
## gdp_per_capita life_expectancy ClimateclassClass A - Tropical Climates
## 1 0 0 0
## 3 0 0 0
## ClimateclassClass B - Dry (Arid and Semiarid) Climates
## 1 0
## 3 0
## ClimateclassClass C - Temperate (Mesothermal) Climates
## 1 0
## 3 0
## ClimateclassClass D - Continental (Microthermal) Climates cum_p_score
## 1 0 0
## 3 0 0Training test accuracy %
# predicting values for train dataset
data_train$cluster_predicted <- predict(model, newdata = data_train, "class")
# building classification table
tab_train <- table(data_train$cluster, data_train$cluster_predicted)
# Calculating accuracy - sum of diagonal elements divided by total obs
round((sum(diag(tab_train))/sum(tab_train))*100,2)## [1] 100Test set accuracy %
data_test$cluster_predicted <- predict(model, newdata = data_test, "class")
tab_test <- table(data_test$cluster, data_test$cluster_predicted)
round((sum(diag(tab_test))/sum(tab_test))*100,2)## [1] 55.56##
## Pearson's Chi-squared test
##
## data: data_test$cluster and data_test$cluster_predicted
## X-squared = 7.0948, df = 4, p-value = 0.131Exponentiate model coefficients
## extract the coefficients from the model and exponentiate
exp(coef(model))## (Intercept) stringency_class2 stringency_class3 stringency_class4
## 1 8.47374e+09 3.674249e-57 2.8827311489 7.213891e-92
## 3 1.46307e-02 5.043372e+01 0.0005699729 3.471380e-25
## excess_death_class2 excess_death_class3 excess_death_class4 persfreedomagency
## 1 1.743941e-13 9.515398e-58 1.789437e-24 8.263259e-02
## 3 1.384680e+19 7.249495e+21 1.318590e+02 1.684545e+59
## Socialcapsocialnetwork healthprevent Socialcapcivic PersonalFreedom
## 1 7.236178e+32 1.544967e+40 1.049321e+08 5.044468e+00
## 3 3.422304e+73 2.536985e+13 6.324756e+02 8.643764e-58
## GovernanGovernmeffect Socialcappersonalandfamily continentAsia
## 1 6.775999e+14 1.978825e-21 1.340571e-04
## 3 4.601367e+00 9.600688e-20 3.297680e+22
## continentEurope continentNorth America continentOceania
## 1 1.263602e+05 6.954010e-16 0.1583607
## 3 1.310103e-16 7.585944e+14 0.2785396
## continentSouth America population population_density median_age
## 1 1.57943 0.9999995 3.207762 2.143744e+01
## 3 38.66745 1.0000071 2.373683 6.975613e-57
## aged_65_older gdp_per_capita life_expectancy
## 1 4.361310e-14 0.9367855 2.315412e+01
## 3 1.545784e-60 0.9796032 1.842435e+24
## ClimateclassClass A - Tropical Climates
## 1 2.355418e-15
## 3 3.801658e+13
## ClimateclassClass B - Dry (Arid and Semiarid) Climates
## 1 6.376833e-03
## 3 5.339854e+05
## ClimateclassClass C - Temperate (Mesothermal) Climates
## 1 1.873178e+17
## 3 1.584454e-13
## ClimateclassClass D - Continental (Microthermal) Climates cum_p_score
## 1 3.011778e+09 1.712319e-06
## 3 4.548658e-09 8.334233e+00## [1] 70